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We prove that each optimization problem associated with finding an optimal straight line distance between two regions of a weighted planar subdivision can be restated as a two-dimensional sum of linear fractionals problem over an arc of the unit circle. Compared to previous results, that involved more general functions over two dimensional domains, our solution has potential for order of magnitude speedups. The problem has a few bio-medical applications, including optimal treatment planning in intensity modulated radiation therapy and brachytherapy.
Date of Conference: June 29 2008-July 5 2008